A microwave filter is an electromagnetic circuit that can be tuned to pass energy at a specified resonant frequency. Accordingly, microwave filters are commonly used in telecommunication applications to transmit energy in a desired band of frequencies (i.e. the passband) and to reject energy at unwanted frequencies (i.e. the stopband) that fall outside of the desired band. In addition, a microwave filter should preferably meet certain performance criteria such as insertion loss (i.e. the minimum loss in the passband), loss variation (i.e. the flatness of the insertion loss in the passband), rejection or isolation (the attenuation in the stopband), group delay (i.e. related to the phase characteristics of the filter) and return loss (i.e. related to the ratio from the reflected and incident power).
When the material type and the size of the resonators for the filter are chosen, the Q (i.e. quality) factor for the filter is set. The Q factor has a direct effect on the amount of insertion loss and pass-band flatness of the realized microwave filter. In particular, a filter having a higher Q factor will have a lower insertion loss and sharper slopes (i.e. a more “square” filter response) in the transition region between the passband and the stopband. In contrast, filters which have a low Q factor have a larger amount of energy dissipation due to larger insertion loss and will also exhibit a larger degradation in band edge sharpness. Examples of high Q factor filters include waveguide (hollow cavity) and dielectric resonator filters that have Q factors on the order of 8,000 to 15,000. An example of a low Q factor filter is a coaxial resonator filter that typically has a Q factor on the order of 2,000 to 5,000.
Dielectric material with high relative permittivity, or a high relative dielectric constant (i.e. typically a dielectric constant greater than 20) are widely used to form microwave/RF resonators and filters. Permittivity is a physical quantity that determines the ability of a material to polarize in response to an electromagnetic field, and thereby reduces the total electromagnetic field inside the material. Thus, permittivity relates to a material's ability to transmit (or “permit”) an electromagnetic field.
Due to the fact that the materials of the various components are dielectric materials, they are very poor in conducting heat. Thus, in high power applications, the temperature of dielectric resonators can be very high, which can cause serious operational difficulties especially in a highly constrained mechanical design space.